What is the hardest part of teaching? part 1

On of the weirdest things about teaching is how aware one ends up of the multitude of contradictions and paradoxes that infuse education, and do so at so many levels. In a sense I think this is an expression of a very deep expression of the complexities and contradiction inherent in adult expectation of children. Parents not only want their children to well, but also want the same children to face down the ghosts those  parents were haunted by a generation before: More than that their kids give then younger eyes on the world again, a world that has shifted from when they were young, a shift they want the education of their kids to reflect (but not too much).
  Moreover the wider adult community is incapable of seeing kids for the tangle they are. It rather resolves them, and what we teach them into crypto mythological debating points, about behaviour and standards, and duties and success and failure:: A constant stream of platitudes from the media/political classes that is about ideology, or perhaps mythology. It is an a series of statements and expressions, tied together in a loose argument (but really a legend) about where WE (Britain) are in the world, and the FEAR about where likely to end up... We as a nation project then our fears of failure on kids, and what we teach them.b All of which in a sense is ok, and natural, but adults are so pompous about all these feelings, and think that they must not confess them to their kids (who know them anyway), or to themselves.... 
From which it follows that the 'debates' we think we are having are frankly senseless or at least so abstract as to become pointless, be they about standards or teaching method or whatever. and the result is of course by and large a lot of pointless meaningless, if passionate discussion, which is more about the society 'living' being a democracy, than it is anything real (and so a myth). It certainly does not really reflect life teaching. The only direct link that exists between the two worlds comes when one of these debates creates a movement in the syllabus which rips though the class room, changing what is taught (and forcing the school to by new products or send teachers on training days - so spend money)... Occasionally one scoops the gold with these reforms. Those of you have read my blog will know I am a fan of the current GCSE syllabus, finance and tax  is so much better when taught by mathematicians who really understand the maths, than it is by any other set of teachers (or at least that is my prejudice). It also allows one to generalise and to show how maths and our treatment of statistics underlines the way we think about society.... but the reform clearly will not last very long, and we will be back to the mythology of teaching soon.
 As a teacher one is therefore attempting to hold down all these fears and allow them expression, while also actually helping individual kids learn about the world they are meant to be learning about. That is the topic one is also trying top teach them. The problem of course is that this topic is so far down the agenda. One has so much more to manage first. For as I said before kids know that what they are being taught has more to do with adult fears and feelings than actual reality, and they really resent it , and why not. It is after all an abuse of power, if one made in the name of education. Getting them through this antipathy and towards what actually matters, and showing them that some of what they are being told is useful and even vital, is for me the hardest part of teaching. The problem is one of trust, as much as anything. A trust that this mythological debate with all its inappropriate passions does not help at all.. The problem is therefore one cut through all the guff to the actual reality of how how helps another person restructure their minds (for that is what teaching really is).
 Or to put it another way, we have created in schools a real paradox. In most human history, myth and education are the same. The myths structure then mind and that is it. But here and now, in our schools, teachers must run counterfactual to this age old truth as they teach. Our knoweldge is almost opposed to the myths we have about it (or at least it is in maths). This single fact makes teaching so very much harder, but if I am honest it also makes it so much more fun!

When is the time to get a maths tutor?

Just in case anyone is thinking shall I get Maths tuition for a summer exam?
 - Now is the time to do (November). Just just before Christmas.
If you wait until February or even even April a tutor will do there best, and make some difference (firming up grades) but it is very hard to make a really significant change as it is hard to cover the entire syllabus in detail, and do the necessary practice for questions. What one can do effectively is therefore restricted (there is only about seven teaching weeks, given easter from end of march on June...)
If you start in November though, everything is still up for grabs. One can make a really big difference, as one can cover all the syllabus, and have time to look at questions in detail.
 So if know you need help, do not wait for the mock in a few weeks time, act now, and make that difference!

What really impressed

I am, as a teacher, always endless impressed by the sheer pluck and commitment of most my pupils. Oh you get some who are time waisting, but very very few. Most do actually want do well, and it is one job as a maths tutor to make sure they do (and know they can). More than that it is also part of the job to nurture this desire, and make it matter, in the face of natural laziness, but also, even more of school expectation.
This desire to achieve is sometimes (well, to be honest in the maths tutors world, it is often), frankly in spite of their school's expectation of what they can do, and were they have been set in class. An expectation that of course a self fulfilling prophecy. For most schools only teaches the full syllabus to those it thinks are up to it, and the rest are often taught much less (so they can only get a C), - and what is more many of my pupils (and their parents) have not been told this fact. One of the jobs of the maths tutor is therefore to tell them this, and see what they want to do. At this point pupils face a simple choice: Do they want to achieve what the school expects or do better? And if they want to do better (and they all want to), are they going to work hard enough to ensure that they will get where they want to be? And what so impresses me about my pupils is that they not only want to do better that they are meant to, but, if suitably inspired, will work hard to do so.
It is my job therefore to ensure that this work makes the difference, and that they can really get where they want to be. It is this aspect of maths tutoring that I love, and that keeps me teaching, and keeps me inspired.

GCSE - and the thrust of the written

When all is said and done - as I have made clear in this Blog, maths is more a game of writing, than counting. Write it in way that tallies with your eyes, and your expectations, and it is clear and easy - but if you do not you have not got a hope.
Yesterday's lessons were a classic example.
 Yesterday's three separate sessions (with maniac drives between in the devon-county dark, with famers harvesting, and forcing me and the transit to reverse half a mile, in the dark....But that aside), illustrate this point very well.
Each of the pupils I saw I taught caught a different aspect of this problem. The first, who was sitting an exam for a second time, in the hope of firming up a C into a B, is in an exam where one needs to experiment greatly with numbers-  and hates it. For him maths is all about getting the answer done (a reasonable proposition - unfortunately one not shared by AQA linker maths GCSE). For AQA numbers are about play and experimentation. The Examiners want you to  pull out formulas which you have never seen, and things you do not know from the maths you do know. To do this one simply has to write down the formulas, and then pull them around, again and again until one gets the answer. It takes a lot of trust, but also a lot of confidence in the fact that one is writing it down right and well. If one does not have either the show cannot get going. The problem for this pupil is, as is so often the case, he does most of this maths on My Maths and no one has ever (well apart from me), really worried him about the writing down of equation (I have always thought he has been taught them by his school in a way to make them easy at the simple level, but so much harder at the level he is now on). The result is that he will not even start to play. He sees what I have done, but cannot get going  himself. What I will do is attempt of the weeks to persuade to starting on the pretext that he 'might get a method mark if he always does this...' - only once we have got going do I think he will turn round and suddenly get it!
The second pupil (three tractor reverses away), is younger and had another version of the same problem. For her it is all about narratives. She understands (although does not belief she understands) the individual calculation quite well. But what she cannot do is tell a story with the figures - and unfortunately she is in an exam (Linear Edxcel GCSE ) which loves its stories. One does not therefore only need to count, but also describe in figures, and keep the narrative going. In teaching her therefore I am still very much trying to explain to her what she cannot do - because she does not really know. What she thinks is that she cannot DO MATHS, what I think though, is that she cannot make maths tell stories.... Once this become clearer to her (and we will need to do a little more method work I think to make it so), then I am optimistic she will be fine, if I can get her through the collywobbles that far.
 My final lesson (another long drive to the coast though back lanes away), same problem, but again in another setting. This one was a pupil half way through a foundation GCSE exam. She had done one exam yesterday (and was very confident), but had others to do. What she lacks, again is the basic ability to know where to being in any question if it is at all complex. She can do perfectly well short questions, but does not want to try longer ones. My break though with her (she is a dancer) was to persuade her that maths is just another performance (which it is). To understand the kind of wordy questions she is having to do in her GCSE exam one needs to role play! That is one needs to pretend the numbers make sense and are about ones own life, and not merely a faceless set of nothings. It was this basic move that made the difference I think for her. It made the numbers feel like something, and do so even when they do not make sense (and actually her mental maths is a little weak).  Once she gets the part, she understands the problem, and how to write it down.
 Three very different pupils, three different solutions, and yet one real problem, Modern GCSE is a game of reading and writing in a  weird way - and one needs to be endless creativity to teach that oddity.

Best of luck!


 So here we go again - it is another exam day (there are so many in a year). This time it is aGCSe: some school are doing the EdXcel Unit exam, while others are taking the full foundation GCSE now, so that they have a chance of retaking it later, or upping their grade to the higher exam. It is an exam school are putting their weaker candidates in, or else those who are out the proof the school is wrong in their setting or treatment of the pupil. I am therefore peculiarly interested in the results, which are due in January.
So keep your fingers crossed today!.

What makes a maths tutor different? Part 1

The second great thing I think one to one maths coaching can offer, is that it alone can actually watch where you go wrong/ i spend my time in tuitions teaching certainly, but also listening y really carefully to what I am being told by my pupil as the work though a problem, but also watching their face and their pens. one therefore spends ones time actually watching thought as it happens - in all its hesitant beauty, and layered complexity.
 The job is then to work out exactly how and when one needs guide the other persons thought process. I personally am a great fan of doing a little as possible, But doing soemthing. I will tap the paper therefore on a sing, or raise an eyebrow, or sometimes re-ask the question. thee point being that i am trying to teach how one notice and then reacts to that observation in maths. the game in the subject is never not to be wrong, but merely to write down in such a way that one naturally notices or looks for ones own error.
If I get the 'correction' right, therefore it should feel like for other individual it is them that is noticing the problem, it is their eyes and their brain - I am merely showing them where and when to do it.
 And yet of course this isa  risky strategy. when it works it is great,but you have to be so careful. It is so easy to not be helpful, and merely be irritating. Each pupil is different not only in the way they  think, and the exact place they make errors, but also, and just as importantly in the way the way they like to locate those errors. one needs then to have also ready the 'stock tutor' methods which allow for one to find errors through very formal writing down of methods - a formality that is certain aspects and at certain times is astounding useful and powerful.
 What maths makes tuition so difficult, and so powerful at times (and given the right relationship), is that one can teach the real brain on skills that gets you through maths exams, skills that one cannot teach anywhere else i think, and ones always worth having - they the skills that allow one to be self critical, and reflexive.

Getting them grade up

What is it that really makes the difference in grades?

This is a question that haunts all maths maths teachers I guess - the job is after all to make a real difference to grades, and so lives.
There are of course many answers to this question.One needs good written methods, one needs patience, one needs confidence..., All of which it is of course the maths tutor's job to add.
And yet the philosopher in me knows this is not really it. What one really needs for maths is rhythm. Maths is a game of noticing, writing, checking and experimenting. Problems then come in maths because no one really teaches (or even seems often enough to appreciate) exactly how one orchestrates these facets of 'doing maths'. This is a real problem, as kids want permission, they crave to be old what to do next, and the point of the maths exam is exactly that one is not told, on has show initiative, and think: One needs therefore to impose ones own rhythm, ones own inner knowledge of what is next (and why). This is genuinely terrifying - it is what scares adults about maths: They never know what to do next....
 It is no surprise that most of the time when a maths teacher is called in it it is because one or other of these elements is out of sync with the rest and the rhythm has broken down. It is your job, as a maths tutors to get them all lined up with one another, as best they can.
 What do I mean when I say maths is rhythm. Only this, to successfully navigate a question, one needs to know what one is doping and when: all too often mistakes happen because one tries to do every at once. Or even worse one gets right, but at the wrong moment, and that stifles ones ability to think what one has done, and actually know what one has worked out. It is only rhythm that defines when one is thinking, when one is looking and when one is writing: whether one is good or not at maths in the end is all about rhythm. A rhythm some kids have innate, and other have to be taught.
 To teach maths one first needs  always to check that pupils know how to notice, think, write and correct, (all of which are real skills in their own right, and again never formally taught) - but in the end grades are made or lost of rhythm. If you know what should happen next, what you should look for, or check or write it is all so much easier.
It is the rhythm that makes the difference between knowing what to do in  question, and seeing that it is so easy, and being at sea with it all. It is therefore the first and last job of maths teacher to give thought rhythm!

Bite Sized

It is a strange feeling, teaching the new maths syllabus.
 On  the hand one is teaching a course that is actually very worth while - in the sense that the maths that allows one to fill in a tax return or work out a fuel consumption is always good, always useful. More than that it, teaching the kind of methods that one needs to work out real world situation demands one actually teaches thought, rather than simple 'you do this then that, then this.' The philosopher me really revels teaching this syllabus, as it really demands pupils think and presents the teacher with the challenge that we teach the links between topics, rather than the formal topics itself.
 On the other hand, it is very very strange to  teach, if one understands teaching in its old formal sense. That definition of teaching was very class room based, and what it taught reflected the classroom situation. One taught methods inside topics and during formal lessons - one did fractions then percentages, then ratios, and left it to minds of the smartest to work out that these are really the same thing. One could use the connection between the different elements of the syllabus as a signifier for smartness: A's were given to those who link topics, and as teachers we conspired that it was so.
 The strangeness for me, is that while the first stratagem for teaching is for me preferable, it is as a teacher much harder to work out both what you are doing, and what the long terms effect of what teaching be. I mean you are teaching to something that is integral to humans, namely their real understanding. The pupils therefore really comprehend what you are saying, which is just as well as the bite sized  ' you do this then that in this case' approach cannot be formally taught as such. There are no simple methods or internal 'one-size-fits-all written answer calculators (that is very few formal written methods). One is therefore never really sure, until the next week or week after, of the power ones teaching:-  If you like one is always flying blind, as one cannot read another's mind, and there nothing on paper to read. If you like maths teaching has become intuitive! Which for my money is no bad thing....
 The only trouble is, of course that this being blind makes the teaching slightly weird for the teacher as it is (potentially) good for the pupil- and problem is that education is run by adults, as is basically for adults: Teaching is so often an expression of adult anxiety, and not what is good to learn. It is then surely only a matter of time before we turn back to what is easy for adults to teach, asses and so judge both pupils and teachers. A fact that makes teaching the new approach all the more odd. I know even as I really get my teeth into how to teach it, how to think it, that the knowledge will soon be useless, and swept away in the interest of tradition.

Leaders....Follow the leaders

It is one of the strange, and very hidden dangers of teaching - any teaching -  namely the problem of power.
 Power is always at stake in teaching; without it the very ability of the teacher is questioned - authority breaks down, and with it trust in what is being taught; and once that has gone, then all teaching ceases: all that are imparted are a random sequence of half truth.
Power matters therefore to teachers, we need it.
And yet, power warps the powerful, of course it does. It is so easy for a teacher to assume that somehow the power they wield is justified and right. All the more so as the power is often hard won, and potentially problematic in itself. It needs therefore to be substantiated, by an assumption that the power is somehow justified and simply 'right';  the implication then being what that power breeds, what abuses or assumptions are also necessarily right.
 Now in the past the relationship was of crisscrossed by voilence. Teacher could wack children and did often. It then went through a period where work itself became the issue. If one wanted to enforce authority, then one made the students work harder, or pointlessly. And now of course we express the same abuse in terms exams, and endless regulation. we make kids feel small, by making them feel stupid: By revealing that stupidity, not only to them, but also their peers...And at the same time of course, on a slightly bigger picture, the 'powers that be' in education (politicians and regulators) wield their own power over teachers. The struggles of kids and teachers, are then caught up in a wider struggle of politicians, with all that entails...
 Of course one has to be so very careful in all this. Power and teaching goes together, of course it does - and power and abuse goes together, just as naturally; for once one has power it is next to impossible to pitch it right. Indeed the anarchist in me thinks it is impossible for power to be otherwise. There is no point, one moment its righteous exercise becomes an abuse. On the contrary, the two sides of power are caught up together, abuses are justified, from other angles, or if the mood music changes...
 The problem any epoch in education faces is therefore where it draws its lines of power - and how it links learning to discipline and so to thought. There is probably no right and wrong here, only exercise and consequence. The fatal mistake that adults make is that kids do know what is happening and why. Of course they do, they are just pragmatists and accept it all - but then of course of judge it and  its justifications in their own way and in their own time. A thought I think that is so difficult for adults to encompass, that they ignore it - much to the cost of the over all system.

tool kit maths

Now I loath myself for sounding like Michael Gove but....

 One of my pet hates is the current craze sweeping primary schools for 'intitutive maths'. Put simply we are teaching kids the hidden structure rules of numbers , to enable then to do division and multiplication. So 7 times 15, becomes 70 plus 35, and they do it all in their head. Or again 480 divided by 5, becomes  450 divide 5 plus 30.
 It means you can give a method very quickly. It gives you also a lovely touchy feely approach to counting. In terms of confidence wonderful them - and I cannot fault it. Likewise as an adult means of counting it is faultless - I might go further the best mathematicians are the ones that see numbers in this way: they feel and love the structure, and we are now teaching it. We are making then 10 years old think like Gauss, and is beautiful in its way,- and if with Gove zeal gets rid of it  I will yell and yell and yell....
 The trouble though, if you are not Gauss (and most ten year olds are not, they are merely playing at being him) - is what the method can not do, and what it does not teach, and what it does not show.
 The first of these problems I always call the sneeze rule. If the method you are following does not survive me putting you off, by sneezing, coughing or simply talking, then it cannot be your only method. I have put off numerous kids using this method, and no one has ever come back and remembered where they are. It might sound trivial, but in the real world a method you cannot pick the threads to if you are made to forget for a moment is louzy. It simply cannot be your only method (Gauss could use it, as he could think so quickly you could not put him off....)
 Secondly, I think it creates the wrong impression of what maths is. The problem kids have is not working things out in their head, but reading and writing. All the trendy methods in the world do not help this fact. They simply do not set out mathematics in a way that helps kids think. We need trendy methods to solve the real problem that algebra (and maths in general) involves writing down not what you are thinking, but what you have thought and are about to think. That is what makes it hard. That is what makes it fun! For there is nothing like it....
 What is more the kids I see, who work things out in their heads all the time, are clueless when we given (as we do the minute they hit secondary school) anything that requires detailed writing. A problem that gets worse again the minute we turn to algebra. The point is algebra  is easier and easier the more you are used to writing stuff down formally. If you like, what makes algebra so great is that it is the naughty breaking of apparently formal and eternal rules. It is the point you break the rules, as you see how they work. We are trying to teach that point rather earlier in the process. Its effect on how you think of an equation is then problematic I think.
 Oh I am not saying there are are not trendy methods to solve equation, there are. I know many. That is not the point though. The problem is rather, that unless we really do produce a generation of kids who can think like Gauss and so see numbers, and can palpably feel their connection with algebra ( and maybe we will - or work out a way to teach as if we did), the methods we are currently teaching will  in the end break down. There are no trendy methods to differentiate equations or complete the square. At some point maths has devolve into a tradition form. I council would be kinder in the long run to kids it we make this change earlier than later -  and sweeter and funnier ( It seems sensible to do it when kids still believe what adults say, and not when they assume adults always lying anyway)...All the more so, as this will help them  cope with the kind of questions that require a lot of writing that have already crept in by 10!
 Finally I spend my teaching life telling kids to write working it  down - as insurance, against getting the answer wrong. It seems then rather rich if we are early on in their career conspiring to prevent writing it down at all!
Now again I am not knocking something in these methods. What they do brilliantly is be on the kids side. They are methods to make maths feel easy, and happy. Great, I am all for that. But the sad old adult in me knows this is not totally the case.We are simply not on the kids side  or not totally. Our exams are often rather opposed to kids, and they know it, and fear it. Putting off the fact that this is so, is not good, let us be honest about it all a little more...
The point here is actually substantitive. What matters in the end, in, maths as we teach (if not live) it, are  written methods. Or to be more philosophical about it, what maths is all about  is the way writing  takes control from the thinker's head  and puts the thoughts onto the paper;  and how in doing so our thoughts are  externalize and simplified, even as we loose absolute control over them.
 So for me the gift of real teaching is getting the kids to trust (and then love) paper. This is not easy, they do not naturally do it. They all want to keep thinking 'in house', and trust their brains, not the their writing, which open them to criticism external and internal. Good teaching, is therefore what allows kids to navigate this potentially difficult process and makes it feel easy ( I find history and stories great at this) : But what they simply do not need is  anything that conspires with their reliance on in house maths. Such maths has its place, and utterly necessary, but it misses the challenge, and simply will not get you through your maths career...
The only thing I can say is perhaps the present craze for chunking and the rest was invented by a maths tutor, such as myself, for we are the only ones going to make good business from it...and that is awful, I ought to be marginal, and scratch around for a living.

What is maths Teaching for?

With maths teaching it seems to me there are two main approaches. The first, the traditional approach, really has Maths down as the great initiation rite of our country. It is the Bar we put up to stop just anyone being anything. You have to be able to solve these random puzzles, some with some relevance to here and how, some dating from Ancient Greece, some from even older than that.... - no matter-   to prove you are one of us.
 This method is good for elites, as pupils very quickly work out whether they are one of us or not. It is good for universities, who ensure that only pupils who can think in a very certain very prescribed way come into to the institutions. It is good for politicians who get an exam they can claim is difficult. It is good for Maths teachers (and tutors), who get an exam that is easy to teach (or next to impossible for the uninitiated). The people it lets down of course are the pupils -most of whom are not able to get those grades, and have to rest content with the fact they somehow it is all their fault.
 The exam then is then very much a passion play, in which a social order based on an arbitrary selection and partial (if highly obscure) merit is re-enacted, and enforced in the same moment. What is lacks any notion is maths as we live as adults with all  richness, and complexities (from filling in tax forms, to guess measurements - its all maths). Rather than any of this  richness we are presented, as a necessary truth, a maths exam that is the stale, sterile exam. the product of empire and tradition, and utterly valueless in itself.

The other approach, the one we have just moved to sacrifices the obscurities of mathematical rigour and the elegancies of of a single exam, for continued modular assessment, using questions that are based on real life adult experience. Now there is a real sacrifice here, if you understand maths only in terms of a tradition exam, where a certain number of universally acknowledged truths must be imparted (or else some one somewhere has failed). The modern exam, with its emphasis of reading and actually thinking, will not have space for such truths. But instead it teaches the really very valuable skills of how one reads different maths questions, how one thinks about them, and one one is reflex about what one is writing.
  The importance (and uniqueness) of this reflexive complex method of reading and thinking is difficult to over emphasize. You see maths needs to be read and written in a way utterly different to the way you read english. Is so many many ways maths reading and writing is unique and different: In maths one reads and reads questions, as one is solving it (and as it starts to make sense); one does not necessarily start at the beginning; one plays with meaning, resolving it careful, part by part, and only at the end creating a whole (which makes sense); one checks the links of algebra and grammar, finding different ways thought can be described; one creates accords between drawing, writing, thinking and reading, accords that are hard to express, but easy to grasp.
In short this is an exam where one must really think and one reads and writes, and do so without let up. What is more one thinks about thins one has a handle on, that one can see are useful, and do matter. In In addition to this the unit version of some of the exams allow pupils to really get the bit between their teeth. They do well in one part of the exam, and suddenly wake up and work. Pupils in such circumstances will start to feel that the exam is for them, and that is enough to make them think differently. It gives them an impetus to engage. It is not then that unit exams are easier, they are not; they merely inspire people to work, people the old exam would necessarily fail....

 Now the exam is messy. It does not produce simple 'product'. Pupils with 'A' might excel at different parts of the rich exam, and so universities (and politicians) can not guarantee what a grade 'means'. Likewise the rest of europe, which has kept the initiation approach, looks on in amazement at the sheer 'wierdness' of our exams (I actually teach European students, who have done very well in the Baccs, but cannot get their head round exams that make you think). It goes without saying that the exam is hard to teach, and so does maths tutors at least no favours.
 But the people who respond well to it are the pupils (and their parents), for them the exam opens out endless new possibilities and new worlds. Is that not the point?

 No of course not.
 The exam is  bad for the social repression element of a maths exam, -  for lots of people, from many different backgrounds, might do well in  it, and we no longer have the select brotherhood of 'mathematicians' (Good I say even as a member of that group). But it is of course this last element, the role of maths in the social institution and enforcement of a particular kind of meritocracy, that really matters. Which is probably why the power that be, when they wake up to the change,  need to suppress it. Maths is our initiation rite. The idea that 'standards have slipped', and the maths of Ancient Greece is going by the board, feels significant, feels like a diminution in some manner, and lessoning of the magic of the old exam, and the power of the initial initiation. And therefore, to defend the status quo, we need to destroy this new exam, and do so even as we deny the reasons why we must do so. Our system of exam-ocracy masquerades as a more open meritocracy, and we would defend it as that.
  The real problem for me at least, is not the defence of a social order, but the  clear political (and anthropological) hypocrisy, that this defence involves. To undermine kids in the interests of a social order is common place (that is what societies do), but we ought at least to be honest about it - and accept the choice between different ways to teach and think about maths, is nothing to do with quality, or merit.

Well - we didknow that it happened

One of the sad facts about the current education security is he has tendency to view with suspicion everything that was not around when he was at school. And so he argues that modular exams, multiple boards, GCSE's all of it, must go, and the clock must firmly be set back fourty years or so, for as Dickens himself said (in the mouth of Simon Tappit)  'it is only in going back we truly go forward'..
 Now it is no that my do not think the current system is problematic. The  endless retakes at A level are a problem, but att GCSE, I think not-  they simply show working hard has its rewards. I have had many pupils who have really tried in a system where they can see themselves improve, and would be lost in the single exam system - which ironically rewards the flyby nights idols individuals who are good at exams (of which there are very many). To change the system is therefore to privileges the idle over the workers....
Likewise the problem of grade poker related to schools swapping boards, is a problem, But its cause in not the exam, but rather the way schools are assessed. Unless we going to abolish (and it might take that) Ofsted, and rework how we understand what schools do, and how we (as a nation) ask them to endless do they do better, we are always going to get the distortions of grade poker (which the driver of grade inflation, not the exams themselves). Grade poker is then the creation of education ministers who want to prove they are doing something, and has little do to with schools themselves. That is why is is such a despicable game!
But in the hubbub of reform something wonderful will be certainly lost-  namely the Brand New maths GCSE. This GCSE is maths as it has never been taught before - for it is the maths we live by and use every day of lives. Maths made real, edgy, difficult, a maths that does not need 'right' answer, only estimates, a maths that allows us to actually understand the world we live in. The radicalness of this approach, and its ability to change pupils lives (once they get the hang of it) is very hard to appreciate. It is no exaggeration to say that for the first time in twenty of teaching I feel like I am teaching something worthwhile, useful and even good. And this will now be swept aside in the name a reform which will set the clock back thirty years or so, and back to a system of examining and thinking about maths that seemed to delight in making it obscure, tricky, abstract, and about as far from everyday life as it is possible to go. Its loss will be heavy.
  But then perhaps it is hypocritical of me to really mind. For one thing is certain, the old system with its sudden death exam was very good for maths tutors. If they reforms go ahead, my business will boom, as it always does when the system does not suit the pupils very well. But I am for at least big hearted enough to see beyond my greed. I just politicians were the same...

Grade Poker - part 2

Let's face it - grade poker is a heartless game. I call it grade poker when pupils face repeated entries into GCSE exams (often beginning in year 10 or even 9), with the sole aim that the school maximises its grades, and so does not face an ofsted investigation. Time after time I first meet a pupil when they are demoralised and  reeling from a particularly inappropriate bout of poker. They have been entered into an exam too early, and before their own personal ability to read, to think and to count, are lined up in the necessary conjunction to sit an exam, The result 'shot across the bows' has nearly sunk them. And I spend weeks getting their confidence up, before ever we open a paper.
 The roots of Grade poker lie I think in the difference twenty years ago or more, between public school and comprehensive. Almost all privates schools played grade poker. But then they had the freedom to do so. The creamed off the best students in the 13+ exams, and got them wired in to a great exam sausage machine straight away - and those who rebelled were asked to leave. The result was that grade poker, particularly when played against 'bog standard' schools, was a very successful game. But then some time in the nineties it was decided that the public school model ought to be unwound for everyone if possible. The Creaming of talent and the ruthless removal of failure were clearly not appropriate in the state schools system-  But grade poker was a game everyone could play.  Everyone who really mattered in eduction (I mean ofsted, government, governors, exam boards,teachers ad even parents) were happy. Here a way to import the public sausage machine into the state system.
 The only people who screamed were the kids - but then of course we could all yell back, that the exam were character building, and anyway to got them off their X boxes..... Well Maybe - but grade poker to my mind has long since stopped being appropriate or funny. Kids are simply too smart for it. They know they are being led through a series of exams, not for their own benefit but for the schools and for the 'collective good'. More than that they know they in the  end the school will not make decisions based on them as living, breathing kids, but merely on the schools own need to get an As. So they  have simply become used to the fact that  their exam  board has to change half way through their course, or that the exam has changed half way through their course or they are 'required' to sit the exam early or late, or miss it or do it in april of over Christmas (all of which I have known in the last three years). Kids then have stoically and to my mind heroically accepted that their education is nothing about them, and is all about the school and the government.
 And yet, and yet, and yet, as I am called to see yet another lovely kid, who needs to get a C to go to farmers academy, and would get it quite easily, in the normal course of things, at the end of a GCSE course;  and yet who is being forced to take the exam a year early, and has the prospect of taking it again and again (unless I can make a difference), and is panicking at the thought;  I start to dream of the old system. You that one with an exam at sixteen - or at least a single set of modular exams, and perhaps even a maths project systems or two, a system that might have been dull, but seldom caused this level of panic. For the current world of perpetual exam, might be good for the government and for ofsted (Michel Gove you note is not talking about changing the exam regime), and is absolutely wonderful for maths tutor like me (it is my bread and butter), but it is loathsome for the people  who really matter-  the kids - and turns what could be fun and certainly (potentially) life changing namely learning (even maths should be engaging) into an endless grind, through a perpetual game of exam poker.

I broke one of the unwritten rules about maths teaching yesterday. Never however much you are tempted contact those people who said they you get back to you, but did not. It is usually because they have not got the results they wanted, and do not want to tell you about it....
 The trouble is then that you can live in a bubble of good results. It is the ones you never hear about you have also to worry about. And I do ( I reckon, from experience, around haf of them are merely inertia on the part of the pupil - they would tell you but....and the other half are those who have not done it).
 The problem of course is that one so wants to make a difference - of course one does - but sometimes it is not possible. The case result in point, was was a weird one-  the pupil had a genius in plausibly being wrong. I mean he was so plausible in not noticing something, or starting from the wrong place, and so generated such plausible readings, that he would catch me out: I would find myself agreeing within him, and only them say No.
The problem was therefore very clearly one of reading  and thinking about the questions for his actauly theoretical maths was rather good. He  misread questions, wanting them to be harder or just different from how they were, and all else followed. The problem then is of course exactly how does one address those who misread in this way? A real teaching problem, and one as unique as the pupil. What one then does is of course ones best. One goes through questions, one teaches lessons to the way they read must be read, one talks about putting distance in between them and the thought, and talks about reflexivity, and the joy of self correction, and does so repeatedly. One talks about the power of reading a question carefully, but also how to read bearing in mind the examiner, and the nature of a questions themselves... Finally one gives them lots a really difficult papers, and trues to get them to think under stress in a way that will get through an exam.
 All of which can work - but with a plausible misheaded thinker it is always touch and go. For they might help, but they do not tackle the real problem. That problem is that the pupils has just mistook the nature of maths. They are thinking of it too abstractly  just at the moment when you need to think of it as a problem-solving enterprise. This means they are quite literally reading it wrong. - they are if you like actually mistaking the nature of Number in the context of a maths exam.  What makes the problem tricky is that the pupil is not wrong. Maths can be abstract, it is just not in GCSE! or to put it better translating something into maths, into the abstract world of symbols is only half the problem. One also has to translate abstract maths into actual questions, and make sure then you meet up.
  It is this the inspired reader could not do - and I could not seem to show him how to do. He got the point that he was reading wrong, and that it was something to do with the way he was thinking about the maths, but could not stop, could not change - and so got a B not an A. Not awful, but he would have got a B without me... A good reminder to me as a teacher than sometimes it does not work, and one has to keep on learning how to teach, and thinking about how to make sure that next time...
 For the pupil? well the grade did not stop him doing what he wanted to do,and he has time to go back to it if he wants to it. Moreover it does happen that only a bolt from beyond, a result cocked up, can give the impetus to really rethink how one thinks (which is never easy). Maybe he needed that result. If he did then the structures I went through with him of how to use maths to think, in terms of questions should help.
  So in the end nothing is lost but parental hope and the dignity that goes iwith it. But perhaps that is not as bad as that to loose.

The second result I got yesterday was an A. Now this was an interesting one. The exam was the easy exam in a three part modular GCSE. So it matters but is only worth 30% of the whole. The pupil was originally forecast a D, so again a real result. But has left us all with a problem. She is now out performing her class (she is bottom to mid range in her setting), so much so that the school (partly because the poker-game now being imposed by an interventionist central government...) wants to change the exam she is in. She is doing well in the modular exam, but the rest of her class need to go on the linear,(end of year)version of the exam. She is therefore at risk of losing her A and having to sit the exam again, because the paper has changed!
 This is of course where it all gets hard. The pupil herself is about the fourth most able natural mathematician I have ever taught - who in spite of 'doing a dizzy blond act' sees the structure of numbers, and can tell you the right answer very quickly and without really knowing how she does it, and does it for sums I have to right down ( her mum I discovered is the same, but never was encouraged at school)! So within reason we can do our worst to her- she can cope! And yet, she is very prone to being disheartened and assuming she is daffy after all.
 The problem is therefore whether she gets promoted out of the set she she in to a set where they are going to stay in the modular exam - but are likely to go quickly be algebraic, and where it will be assumed, that she, prompted as she is form 'down below'  is daft when she does not understand stuff in the same way. Moreover the move would mean she would loose the teacher who she is rather fond of, and works  well with, and be seperated from all her mates. So this is clearly a no brainer, I told her mum, keep her where she is happy, where she is a star, and do so even though it means that she will be being taught for a different exam from the one she wants to take. The difference between the two papers is actually rather small. Indeed I think with my teacher head on she will probably do better as a result of this move, and the fact that now the school is going (apparently) to enter her in to two exams at once - both versions! It will give her two chances.
   But it will do so only if we can keep her motivated, and wanting to do well, and keep her sprits us in the face now of two exams in the summer. This might be difficult, and yet it is better than the alternative, of a promotion to a class where the Dizzy Blond will take over in the face of algebra, or simply pulling her out of an exam she is on target to get an A in and into an exam where she has all to prove all over again. It all should be possible, and yet it does mean I will have my work cut out, and - will keep you posted.
 But more than that it explains the problem of  any exam system (and all reforms) - they only work sometimes - and easily do not pick the most able students if those students are not typical, and do not know that they are any good (and why should they)! They are the ones thatall too easily get lost, and left to  assume they are daffy.... it is only I think when this happens in the second generation, that they picked up because their parent is desperate that the same does not happen to their kids as did happen twenty years ago or so to themselves....

More Results

So the great ring round produced two more  results.... This time B and an A, both with a story behind them.
 The B grade (Apparently 'nearly' an A) was from a student you I had seen for a year. She had been forecast  a D, taken off the modular version of the exam, and moved from the higher paper to the foundation - hence the mum called me. The school was of course playing 'grade poker'. They were simply trying to ensure she go at least a C (or their own purposes - pupils failing does not look good). The pupil was therefore when I  first saw her throughly demoralised, and already  justifying why she was such a failure....and yet, and yet  I soon discovered she was quite good at maths.
 My aim in teaching her was therefore not really one of instruction - to be honest she already knew and understood it all. The task was rather to allow her to feel she was good (again) at maths, and give her the space to recover the shock of the degrade. More in particular the immediate job was to ensure that her ability to read (which in lay life was formidable) was carried over into her maths ability- because that was what has slipped: Her apparent failure had meant that she somehow was now ashamed to be a 'reader' - and assumed reading was somehow shameful in a maths exam....The immediate target was a foundation exam in January, which she got a C in. That actually was easy once I got her up and reading (that took a few months), and really she did the rest, I was just the appreciative audience!
 The much more difficult task was to get that grade up in the full exam she was now taking in June. She wanted -I checked with her when her parents were away -  a B, and wanted it quite a lot, but not desperately, she was happy with the C..... which meant she was more relaxed at least. Trouble was by now in terms of her maths and reading, if I could get them union I knew she really ought to get an A. But here there was an added problem - namely the new exam with its emphasis of scary long real world questions, where there are no rights or wrongs. None of us had ever taught an exam that looked like this, and I had no idea how pupils would react to it. Again technically (if it was not maths) she would be good at that kind of idea -  but in maths? It felt tricky...
In the end She and I kept her going and kept her trying through successes and failures in mocks, and through a perplexing exam, and she did it (for herself - which is what matters).
The result was  probably very fair. She got a B and was delighted, all the more so because it was just off (like 3 marks) an A - and so much better than she thought she would do, and has convinced she really can do it - and so she was clever after all: she Could Do Maths! So a real result. Her motehr was likewise so grateful, and so chuffed.
And that is actually of course all that really matters. It is only us grown (nerds) who get obsessesed  with those grades and regret the missing 3 marks....

Here we go!
 it is that time of year - the one that I always dread most. It is the day that I will contact all tuitions from last year and find out how they did, and arrange for tuitions for this year, if they still need them.
  I dread it on so many levels. Firstly it is simply the case that I do not know as yet how busy I am next week, in some years the start has been so slow, while in other years I have started with such a bang, it is not true..... So who knows? Secondly I always want my pupils to do their very best - and teach them to do that, and so actually finding my out results is as nerve wracking as if they were my own results, and this my GCSE year,,,. I actually dread knowing-  though i must know.... Finally I guess it is natural to fear the kind of phone call you do not know the result of even as you make it. I mean no one has ever been nasty-  in fact usually the calls the nicest I make all year. People are often happy to hear from me, and curious about the summer - and that is wonderful, but  never assume it is the case, I am just a maths teacher after all!

And yet I still the fear calls. So think of me, and all other tutors today and tomorrow, andkeepyour fingers cross....

It is that time of year again - the time one updates all ones profiles in Tutor Registers for the new year. I have a very conservative approach to this - I have used the same form of words for years, because it tells the truth, and works!
  And yet this year I have added a new paragraph, which reflects the change in GCSE maths. The exam is now more about english than maths. It is a reading exam, and I spent a lot of last year thinking about how one reads questions the often tortured prose maths GCSE and A level is written in (which is ironic as I am very badly dyslexic-  but hey that make me very good at thinking about ways to read of problem). The importance of this cannot be over emphasised - the difference between an A and a B grade isa  difference in ones ability to read the question!
 My profiles have therefore all been updated to make this point....

Making that Difference

   So last night I got the first result I thought - 'hmm, should have done better' at. The result in question was a B, for a pupil who in the mocks got an E - so on the face of it - fine. And yet, and yet, he should have got an A, at least that was what I thought - that was what he was working to in the sessions.
   The problem is of course the ghost that haunts maths tuition, the one I seem to spend my life exorcising and thinking about. The simple fact is that pupils behave differently in tuitions than they do in exams and under the 'pressure' of an exam; and this was a pupil who had this track record of under performing. The game was therefore to ensure that he knew the sorts of questions well enough, and had enough practice, enough mathematical 'bottom', to fight the gremlins of 'sitting the exam', which given that the second exam this year (a calculator paper) was very tricky, was certainly needed. Hard exams require bottom (call it confidence if you like), and he now had it, so did not go to pieces, and yet, did not keep it enough to perform to grade.
   My beef (with myself) is that I should have done better. At issue here, is one of the real arts and mysteries of teaching. Put simply, teaching 'how to answer questions' is a dark science. To take in a 'perfect answer'  is as bad as to try to get pupils to questions they simply cannot do. The game is always to start them off, and get them sparking, get them thinking for themselves - asking the right question, and moving the perspective around, and showing them how one does it and why. In short it is to get them thinking -  and most of them, bless them, all can do that. The trouble of course is how they then react to the fact they are 'thinking'. Many are frankly scared by it. They are not used to it, and are forever coming up with reasons why they cannot really think, if you are not in the room, and say so even as they are working through the questions themselves. I think the question here is really one of trust and the courage that goes with it. To think is to risk one's own genius, and to trust the examiner with that genius, and perhaps with some justification (given how GCSE maths appears to be something of a political football at the moment) they are simply very very unwilling to do this. However good the pupil is, one has to work through this scruple and this fear, and I do so. The risk is that a hard exam knocks them back into 'form'. That is to say, all those doubts re-surface, and the entire issue becomes impossible again...
   This I am sure, happened to this pupil. Hence the lack of an A. The B is then the result of the fact that I taught him well. That is, well enough even under strain not to go to pieces, and to do those bits he could (a vital second line defence). Meaning that I think I did him good (well if you look at his form I am sure I did), and yet, and yet, I still regret that fact that I did not get that 'virtual catechism' which  typifies 'thinking in a maths exam', quite internal, quite strong, enough.
   So that I am left with this feeling that I must do better next time - and am working out how now. For even after twenty years, I feel that I am still learning how to teach - and hope I never stop learning.

To find out more and me and my teaching practice see my website at:

http://www.cartwheels-collective.co.uk/And_Maths_Tuition_too....html

So Results slowly coming in - so far of the four I have got, there are three A's and a C. the C is in a foundation exam (so is maximum mark) and the pupil was forecast an E (or F) - and one of the A's was avery able pupil, who was - without much school help) taking the exam 2 years early (He is fourteen). More results (and analysis) will follow over the next few days.... As I get them (you always get the real shockers first - but others will come)

Hold Onto your Hats.

 Today is one of the defining days of a maths tutors calendar - It is GCSE results day - the day you get to know how you did last year - the day that defines the kind of work you get next year. One of the things I actually enjoy about teaching one to one sessions is it is relatively easy to tell how good you are-  more than that parents can tell as well. If you go off form, you loose business - and conversely if you are good you get busy!. If find it keeps me keen, and sharp, and always going my very best for my pupils....
 So may fingers are firmly crossed for today - good luck everyone-
And if you find your self in need of more maths - you can find me at: http://www.cartwheels-collective.co.uk/And_Maths_Tuition_too....html

Starting the New Term

It is that time again - The time I start slowly pulling off the summer lethagy and thinking about maths result (A Level next week-  GCSE the week after). I am always rather nervous asIi like to do well (I have dual targets for all my students, the first one what I think they would have got without me, the second what they got with me...).
This year I am planning to post these result here, for all to see....
So here we go -
And good luck everyone.